EconPapers    
Economics at your fingertips  
 

Operators and Boundary Problems in Finance, Economics and Insurance: Peculiarities, Efficient Methods and Outstanding Problems

Sergei Levendorskiĭ ()
Additional contact information
Sergei Levendorskiĭ: Calico Science Consulting, Austin, TX 78748, USA

Mathematics, 2022, vol. 10, issue 7, 1-36

Abstract: The price V of a contingent claim in finance, insurance and economics is defined as an expectation of a stochastic expression. If the underlying uncertainty is modeled as a strong Markov process X , the Feynman–Kac theorem suggests that V is the unique solution of a boundary problem for a parabolic equation. In the case of PDO with constant symbols, simple probabilistic tools explained in this paper can be used to explicitly calculate expectations under very weak conditions on the process and study the regularity of the solution. Assuming that the Feynman–Kac theorem holds, and a more general boundary problem can be localized, the local results can be used to study the existence and regularity of solutions, and derive efficient numerical methods. In the paper, difficulties for the realization of this program are analyzed, several outstanding problems are listed, and several closely efficient methods are outlined.

Keywords: Feynman–Kac theorem; Lévy processes; affine processes; quadratic term structure models; European options; barrier options; American options; fractional differential equations; method of lines; smooth pasting principle; sinh-acceleration (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
References: View references in EconPapers View complete reference list from CitEc
Citations: Track citations by RSS feed

Downloads: (external link)
https://www.mdpi.com/2227-7390/10/7/1028/pdf (application/pdf)
https://www.mdpi.com/2227-7390/10/7/1028/ (text/html)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:gam:jmathe:v:10:y:2022:i:7:p:1028-:d:777760

Access Statistics for this article

Mathematics is currently edited by Ms. Patty Hu

More articles in Mathematics from MDPI
Bibliographic data for series maintained by MDPI Indexing Manager ().

 
Page updated 2022-04-30
Handle: RePEc:gam:jmathe:v:10:y:2022:i:7:p:1028-:d:777760